Math Homework Tip for week of September 23, 2013

Comparing and Order Fractions and Decimals—To compare fractions with the same denomiators, compare the numerators.  To compare fractions with the same numerators, compare the denominators.  When comparing mixed numbers, compare the whole numbers first.  If the whole numbers are the same, then compare the fractions.  If the denominators are different, find a common denominator and then compare.

For example:

5 5/8 < 5 2/3 < 6 ½

5 5/8 = 5 15/24

5 2/3 = 5 16/24

When comparing a decimal to a fraction, rewrite the fraction as a decimal, then compare.

For example:

¾ and 0.8

¾ = 0.75 and 0.8 =0.80

0.75 <0.80 so ¾ < 0.8

 

Multiply Fractions:

When multiplying fractions, multiple the numerators and then the denominators and simplify.

For example:  2/3  x 3/5 =6/15 = 2/5

When multiplying mixed numbers, change the mixed numbers to improper fractions and then multiply and simplify.

For example:

1 ¼ x 1 2/3 = 5/4 x 5/3 =25/12

25/12 = 2 1/12

 

Properties of Operations

Commutative Property of Addition—if the order of terms changes, the sum stays the same.  12 + a = a + 12

Associative Property of Addition—when the grouping of terms changes, the sum stays the same.  5 + (8 + b) = (5 + 8) + b

Identity Property of Addition—The sum of 0 and any number is that number.

0 + c = c

Commutative Property of Multiplication—if the order of factors changes, the product stays the same.

d x 9 = 9 x d

Associative Property of Multiplication—when the grouping of factors changes, the products stays the same.

11 x (3 x e) = (11 x 3) x e

Identity Property of Multiplication—the product of 1 and any number is that number.  1 x f = f

Distributive Property—multiplying a sum by a number is the same as multiplying each term by the number and then adding the products.

5 x (g + 9) = (5 x g) + (5 x 9)

Math Homework Tip for Week of August 26, 2013

Adding and Subtracting Decimals-When adding and subtracting decimals make sure to line up the decimals points before adding or subtracting and then just bring down the decimal point into the answer.

For example: 2.567
+ 21.3__
23.867

Algebraic Expressions- An algebraic expression is a mathematical phrase that includes at least one variable. A variable is a letter or symbol that stands for one or more numbers. Students will be asked to write algebraic expression for word expressions.

For example: 11 more than e is 11 + e.

Identify Parts of Expressions- In this lesson, students will be asked to identify parts of an expression.

For example: 5m + 2n
The expression is the sum of 2 terms. The first term is the product of 5 and m. The second term is the product of 2 and n. Word expression: the sum of 5 times m and 2 times n.

Math Homework Tip for Week of August 19, 2013

Greatest Common Factor (GCF)-The greatest common factor or GCF is the greatest factor that two or more numbers have in common. The greatest common factor of 16 and 20 is 4. To find this first list all the factors of each number:

16: 1, 2, 4, 8, 16
20: 1, 2, 4, 5, 10, 20
Then circle all the factors that the numbers have in common. The GCF is the greatest factor that the numbers have in common.
Exponents-You can use an exponent and a base to show repeated multiplication of the same factor. An exponent is a number that tells how many times a number called the base is used as a repeated factor. For example: 5 x 5 x 5 = 53
Numerical Expressions-A numerical expression is a mathematical phrase that uses only numbers and operation symbols. For example:
4 x (8 + 51). You evaluate a numerical expression when you find its value. To evaluate an expression with more than one operation, you must follow a set of rules called the order of operations. A way to remember these is Please Excuse My Dear Aunt Sally. (Parenthesis and Exponents, Multiplication and Division, Addition and Subtraction)
4 x (8 + 51) = 52

Math Homework Tip for Week of August 12, 2013

Prime Factorization–A factor tree is one method of determining the prime factorization of a number. The method is based on writing a number as a product of two factors, each greater than 1. Each of these factors is then written as a product of two factors, each greater than 1. The process continues until each factor at the end of a “branch” is a prime number. Every whole number greater than 1 has a unique prime factorization. The prime factorization of 40 is 2 x 2 x 2 x 5, regardless of the pair of factors used in the first step.

40

4 10

2 2 2 5

Least Common Multiple—A least common multiple is the least nonzero number that is a multiple of two or more numbers. One way to find the least common multiple is to make a list of the first eight nonzero multiples of each number. Then, circle the common multiples and finally find the least common multiple.
For example:
Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48
Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64
LCM= 24

Math Homework Tip for Week of August 5, 2013

This week we will be working on divisibility rules and prime/composite numbers. Your child should have a page with all of the divisibility rules on it (apple page). For extra help at home, ask your child to tell you how they know if a number is divisible by each number. For example,
Parent: “A number is divisible by two when . . .”
Child: “it ends in an even number like 0, 2, 4, 6, or 8.”

I have included a copy of the divisibility rules page on the back of this newsletter.

We also will be working on prime and composite numbers. Prime numbers are numbers that only have 2 factors—1 and itself. For example: The number 3 is prime because its only factors are 1 and 3 (1 x 3 = 3). However 4 is composite because its factors are 1, 2, and 4. ( 1 x 4 = 4 and 2 x 2 = 4).

Super Chunk it Math

We are starting to divide four-digit dividends by two-digit divisors in math.  We are just beginning this using Super Chunk it Math.  You can go to You-tube and search for Super Chunk it Math Division and find videos that explain how to do this process.  Basically, the student makes a chart using the divisor and repeated addition.  Then they use the chart they made to solve the division problem.